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Aug 25, 2024
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2021-2022 Catalog [ARCHIVED CATALOG]
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MATH 211 - Calculus I
PREREQUISITES: Demonstrated competency through appropriate assessment or successful completion of MATH 136 - College Algebra and MATH 137 - Trigonometry with Analytic Geometry
CREDIT HOURS: 4
LECTURE HOURS: 4
DATE OF LAST REVISION: Fall, 2020
Reviews the concepts of exponential, logarithmic and inverse functions. Studies in depth the fundamental concepts and operations of calculus including limits, continuity, differentiation including implicit and logarithmic differentiation. Applies differential calculus to solve problems in the natural and social sciences, to solve estimation problems and to solve optimization problems. Applies differential calculus to sketch curves and to identify local and global extrema, inflection points, increasing/decreasing behavior, concavity, behavior at infinity, horizontal and vertical tangents and asymptotes, and slant asymptotes. Applies the concept of Riemann sums and antiderivatives to find Riemann integrals. Applies the fundamental theorem of calculus to solve initial value problems, and to find areas and volumes and the average values of a function.
MAJOR COURSE LEARNING OBJECTIVES: Upon successful completion of this course the student will be expected to:
- Solve problems using the fundamental properties of the elementary functions.
- Solve problems using the fundamental concept of inverse functions.
- Calculate the limit of a function at a point or at infinity using the limit laws.
- Use limits to find asymptotes.
- Find the points at which a function is continuous or discontinuous.
- Use the rules of differentiation to find the first and higher order of derivatives of elementary functions.
- Find the derivatives of inverse functions.
- Use implicit differentiation and logarithmic differentiation to find derivatives.
- Apply differential calculus to solve problems in the natural and social sciences
- Determine if a given function satisfies the hypotheses of Rolle’s Theorem and the mean value theorem.
- Apply the mean value theorem to solve estimation problems.
- Apply differential calculus to solve optimization problems.
- Apply L’Hôpital’s rule to calculate limits.
- Apply differential calculus to sketch curves and to identify local and global extrema, inflection points, increasing/decreasing behavior, concavity, behavior at infinity, horizontal and vertical tangents and asymptotes, and slant asymptotes.
- Find antiderivatives of elementary functions.
- Calculate definite integrals as the limit of Riemann sums
- Calculate definite integrals by evaluating antiderivatives.
- Use the fundamental theorem of calculus to solve initial value problems.
- Use the fundamental theorem of calculus to find areas between curves, volumes of solids, volumes of solids by cylindrical shells and the average value of a function
COURSE CONTENT: Topical areas of study include - Functions
Local and global extrema
Continuity
Optimization
Limits
Rolle’s theorem
Derivatives
The mean value theorem
Rules of differentiation
Antiderivatives
Logarithmic differentiation
Riemann sums
Implicit differentiation
The fundamental theorem of calculus
Higher order derivatives
Initial value problems
L’Hôpital’s rule
Areas and volumes
The average value of a function
GRADING POLICY
| A |
90-100 |
| B |
80-89 |
| C |
70-79 |
| D |
60-69 |
| F |
0-59 |
Course Addendum - Syllabus (Click to expand)
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